Momentum and Newton’s laws of motion

Mass and Inertia

Mass is a fundamental property of matter. It measures how much matter an object contains and determines how much an object resists changes in its motion (inertia). The greater the mass, the harder it is to change the object’s velocity.

Newton’s Laws of Motion

First Law (Law of Inertia)

An object remains at rest or moves with constant velocity unless acted on by a resultant (net) force.

Second Law (Law of Acceleration)

The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass. The direction of acceleration is the same as the direction of the resultant force.

Where:

• $F$ = resultant force (N)
• $m$ = mass (kg)
• $a$ = acceleration (m s$^{-2}$)

Third Law (Law of Action and Reaction)

If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

Linear Momentum

Linear momentum is a measure of the motion of an object and depends on both its mass and velocity.

• $p$ = momentum (kg m s$^{-1}$)
• $m$ = mass (kg)
• $v$ = velocity (m s$^{-1}$)

Momentum is a vector quantity (it has both magnitude and direction).

Force as Rate of Change of Momentum

Newton’s second law can also be expressed in terms of momentum:

This means that force is equal to the rate of change of momentum with respect to time.

Weight and Gravitational Force

Weight is the force exerted on a mass by a gravitational field. On Earth, this is the force that gives objects their “heaviness”.

• $W$ = weight (N)
• $m$ = mass (kg)
• $g$ = acceleration due to gravity ($\approx 9.81$ m s$^{-2}$ on Earth)

Key Points

• Mass is a measure of inertia.
• Resultant force causes acceleration in the direction of the force.
• Momentum is conserved in the absence of external forces.
• Weight is a force, not a property of the object itself.